1. Find solutions for the divergence and curl of the vector field vat (1, 0, -1). v (x,y,z) = x²z²i + xyzj + z cos(y¹) k

Q: Show that the series converges. Determine the smallest number of terms required to ap- proximate the…

A: 1st we will check given series satisfying condition of alternating series  convergence test or not…

Q: -t 3 denote the centre of a group G. then show that 1 € 3 iff N(a) = 6. so show that if G is finite,…

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Q: Suppose the class equation of a group G is |G| = 1 + 4 + 5 + 5 + 5. Show that G has an element of…

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Q: 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =

A: Given that     gcd(x,y) = 5 ;   lcm(x,y) = 200   and  x-y = 15 Formula :     xy =…

Q: 3) 79 using Gauss's Lemma

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Q: dm dx Prove that: — m „¸a- '2F₁(a,b;c;x)]=(a)_xª−¹ ₂F₁(a+m,b;c;x)

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Q: Consider the transformation T: M₂2 → M22 defined by T(A) = AB, where -2]. Find basis for the kernel…

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Q: Show that if p = 1 (mod 4), then x² = -1 (mod p) has a solution given by the least residue (mod p)…

A: Given: p≡1 mod 4We need to prove that x2≡-1 mod p has a solution given by the least residue mod p of…

Q: -prime and m = mmm Then f(x) = 0 (m) has a solution if the congruences f(x) = 0 (m) has a solution.…

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Q: 1. Define f(x) = & Prove that f: R→ R is continuous. if z 20 -2² if r ≤0

A: Given: fx=x2if x≥0-x2if x≤0 Using sequences we have to prove that f:R→R is continuous.

Q: Saul Goodman tells you that you inherited $300,000 from your Great Aunt Birgit. Under Saul's advice,…

A: Total amount of money$300,000 Rate of interest 4% compounded quarterly Pays out amount =$6,500

Q: Let a and b be positive real numbers. If a, A₁, A2, b are in arithmetic progression, a, G₁, G₂, b…

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Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

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Q: 3. The victims of a certain disease are classified into three states: cured, dead from the disease,…

A: As per the rule of Bartleby we can answer 3 subparts at a time, please repost other subparts…

Q: 1. Show that the functions sin x, sin 2x, sin 3x, . . . are orthogonal on the interval (0,7) with…

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Q: If a, b, c are in A.P., then prove that the following A.P. (i) a²(b + c), b²(c + a), c²(a + b) 1

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Q: Use the simplex method to maximize the following: Maximize f 3x1 + 9x2 subject to 4x1 + x₂ < 5 2x1 +…

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Q: 1. Ytt = 4yxx, 0 0; y(0,1)= y(л,t) = 0, y(x,0) = sin 2x, yt (x, 0) = 0 10

A: Since there are two questions, therefore find the solution of the first question.

Q: Suppose a bank offers you a 5.1% interest rate on a 25-year mortgage to be paid back with monthly…

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Q: Evaluate the following summations. (e) Σ2000 (2+3k). k=0 200 (f) Σ% 2 · (1.01).

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Q: Find the equation for the parabola that has its focus at the (−7/4,−9) and has directrix at x=15/4

A: Here we have to find equation of parabola with given focus and directrix.

Q: Use the Newton-Raphson iterative method to find the root of the function f(x) = x³ + x² + 4x + 3 in…

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Q: Find the first two iterations of the Gauss-Seidel method for the linear system x₁ + 3x₂ 3x3 = 2…

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Q: Prove that : a-l [xª-¹*m ₂F ₁(a,b;c;x)]=(ª)_xª~¹ ₂F₁(a+m,b;c;x) [.

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Q: an be in G.P. with common ratio I the terms a₁, A2, A3, Sk denote the sum of first k terms of this…

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Q: 2. Determine the general value of the following. tan(2 - 5j)

A: According to the guideline, only one question can be answered. Please repost other question…

Q: decide what conclusion, if any, can be reached from the given hypotheses and justify your answer.…

A: Hypothesis: It is an idea which is based on a fact which is not proven. In the given question, there…

Q: Are the following statements true or false? ? 1. K5 is planar 2. K2,3 is not planar 3. K4,5 is…

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Q: rove that let p be a prime and f(x) = ao + a₁x + a₂= e such that an ‡ 0 (p), then the polynomial…

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Q: Show that the transformation 2 = ln x transforms the differential equation 2 x ²³y" + Axy' + By=0…

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Q: Show that if A is square, then |detA| is the product of the singular values of A

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Q: Consider the following differential equation. Let M = y5y² sin(x) - My = Nx = (x-y5+ y² sin(x)) dx =…

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Q: et p and q be propositions. Write the following propositions using p and q using connective: p: you…

A: Given statements P: you drive over 100kmph q: you get a speeding we want to write the following…

Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y, z) = 3x + 4y + z, subject…

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Q: ||projn (x) || = x. n |n||2 || n x. n |n||²

A: Given:  projnx=x·nn2n=x·nn2n. To do: We have to explain how the expression factored out.

Q: R i. Prove every element of Q/Z is a torsion element ii. Recall that the cyclic submodule generated…

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Q: Consider the following differential equation. (2x - 1) dx + (7y + 4) dy = 0 Let M = 2x - 1 and N =…

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Q: A. Verify if the given equation is a solution of the given differential equation: (Show your…

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Q: Find the vol. of the solid generated by revolving the region bounded by the graphs of the eq. about…

A: Given: Solid generated by revolving the region bounded by graphs of the equation about the line y=4…

Q: Find a potential function f for the field F=e4y+52 (3 i+ 12xj+ 15x k). A potential function is…

A: Since both questions are different. So as per our guideline, we are supposed to solve only one…

Q: 5. Use the principle of mathematical induction to complete the proof that the number of rays…

A: Kindly refer to Step 2 for the solution.

Q: Which of the following points can be found on the line 2y = 3x + 4 Which of the following lines are…

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Q: II. For every odd prime q, define M₁ = 29-1. Let p be a prime divisor of Mq. 1) Prove that ord,2 =…

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Q: u = (2,-5) and v= -3i+ 7j COMPUTE: 1. proj, u MADE WITH

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Q: Question 3. Let S denote a solid with the shape of a right circular cone of height h and radius of…

A: We need find equation of cylinder in cartesian co ordinate system and then convert that into…

Q: t (e) ite a4 in terms of a3. Then write a4 in terms of ao. When writing your answer, use a3 for a3…

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Q: Mdzy d+² = Му-кан Determine the position. y of the object at time + if Y it is dropped from a…

A: Md2ydx2=Mg-kdydty0=y0

Q: A group G acts faithfully on a set S if g * s = s for all s € S implies g = e. Show that G acts…

A: Proof 1: If G acts faithfully on S then mg≠mg', where g≠g' ∈G. Let G acts faithfully on S. Assume to…

Q: For what value of n, and b? an+1 +bn+1 a" +b" is the geometric mean of a

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Q: Determine whether u and v are orthogonal, parallel or neither. 33 u = (2, 18) and V =

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